Express the following as the sum of two odd primes.
24

Answer

To express 24 as the sum of two odd primes, we can follow these steps:

### Step 1: Identify Odd Prime Numbers Less Than 24
First, we need to list all the odd prime numbers that are less than 24. The odd prime numbers are:
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23

### Step 2: Find Combinations of Odd Primes that Sum to 24
Next, we need to find pairs of these odd primes that add up to 24. We can do this by checking each odd prime number and seeing if the difference between 24 and that prime number is also an odd prime.

1. **Starting with 3**:
- 24 - 3 = 21 (not prime)

2. **Next, 5**:
- 24 - 5 = 19 (prime)
- So, one pair is (5, 19)

3. **Next, 7**:
- 24 - 7 = 17 (prime)
- So, another pair is (7, 17)

4. **Next, 11**:
- 24 - 11 = 13 (prime)
- So, another pair is (11, 13)

5. **Next, 13**:
- 24 - 13 = 11 (already counted)

6. **Next, 17**:
- 24 - 17 = 7 (already counted)

7. **Next, 19**:
- 24 - 19 = 5 (already counted)

8. **Finally, 23**:
- 24 - 23 = 1 (not prime)

### Step 3: List All Unique Pairs
From our calculations, the unique pairs of odd primes that sum to 24 are:
- (5, 19)
- (7, 17)
- (11, 13)

### Conclusion
Thus, we can express 24 as the sum of two odd primes in the following ways:
- 24 = 5 + 19
- 24 = 7 + 17
- 24 = 11 + 13